We present here the super Minkowski spaces (with minimal supersymmetry) and the associated super Poincaré groups for the dimensions \(1+2\) , \(1+3\) , \(1+5\)  and \(1+9\) : they admit particularly beautiful representations since each of these dimensions is associated with respectively: \(\mathbb {R}\) , \(\mathbb {C}\) , the quaternions \(\mathbb {H}\)  and the octonions (or Cayley numbers) \(\mathbb {O}\) . They are the only normed division algebras and have increasing dimensions and complexity: \(\mathbb {R}\)  and \(\mathbb {C}\)  are commutative fields, \(\mathbb {H}\)  is a non commutative field and \(\mathbb {O}\)  is not associative nor commutative. A good presentation of octonions can be found in [1]} (see also §REF ). In the following we set \(\mathbb {K} = \mathbb {R}\) , \(\mathbb {C}\) , \(\mathbb {H}\)  or \(\mathbb {O}\)  and \(k:= \hbox{dim }\mathbb {K}\) .
